In some situations, it may be useful, or even necessary, to transmit signals below a prescribed spectral energy, for example, to avoid interference with other signals being transmitted in a particular band. One way of doing this may be to use direct-sequence spread-spectrum (DSSS) techniques. DSSS may be used to spread the energy of a transmitted signal over a broad spectrum to avoid interfering with, or being interfered with by, other signals present in the same spectrum. The spreading may be achieved at the transmitter by multiplying a symbol stream by a spreading code, e.g., a pseudo-random spreading code, at a higher chip rate than the symbol rate, where a “chip” is a symbol of the spreading code. The spread sequence may be pulse-shaped to limit spectral emissions by applying a filter to the chips.
At the receiver, the DSSS signal often appears below the noise floor, and it is this low power spectral density that provides the interference tolerance discussed above. A DSSS receiver may correlate the received signal against the spreading code, and a pulse-shaping filter, which may correspond to the pulse-shaping filter used at the transmitter, may be applied (e.g., if a pulse-shaping filter was used at the transmitter). This is often referred to as “chip-matched-filtering” (CMF), and may be used to maximize the received SNR in white Gaussian noise.
However, in the absence of some form of symbol synchronization between transmitter and receiver, the symbol instants may generally be unknown at the receiver. Consequently, the symbol instants may need to be estimated from the signal itself. In addition, the oscillators on the transmitter and receiver are often mismatched, which may result in a non-fixed symbol sampling requirement at the receiver, as well as unknown carrier frequency and phase offset. Typical methods of symbol timing may use a timing (phase) detector and a phase-locked loop (PLL) connected to some sort of adjustable sampling device (e.g., a sample switch or adaptive resampler).
However, symbol timing synchronization may be difficult when the symbol energy to noise power spectral density (referred to with the symbol Es/N0) is less than unity, or negative in terms of decibel units. In such cases, a PLL cannot be used because the loop SNR may be too low to maintain lock. In fact, in such cases it is often difficult to even detect that a signal is present.
One approach to the signal detection problem in unknown carrier offset conditions may involve non-coherent integration (NCI), an operation that may accumulate the magnitude of a signal at symbol-period intervals. Mathematically, the NCI can be described as
a.
            r      nc        ⁡          (      k      )        =            1              N        nc              ⁢                  ∑                  n          =          0                                      N            nc                    -          1                    ⁢                                d          ⁡                      (                          k              -                              nT                s                                      )                                      
where k is the current NCI output sample, Ts is the symbol period in samples (i.e., spreading code length (per symbol) in chips×samples/chip) and Nnc is the NCI length. The magnitude of a complex sample is defined as the square root of the sum of the squares of the in-phase (I) and quadrature (Q) components, but it may also be implemented as a magnitude estimator.
If enough symbols have been integrated non-coherently, and if the oscillator mismatch and resulting timing slip does not cause the samples to become misaligned with the symbol period over that number of symbols, then the NCI may exhibit peaks at the appropriate symbol timing instants. In that case, these timing instants may be used to extract the symbol information in the despread stream.
However, for the case of oscillator mismatch, the samples may become misaligned. As a result, the NCI length may be limited because the peaks may become “smeared” over multiple samples, with the result being that the best timing instant may become obscured. To prevent significant smearing, the amount of integration Nnc may be limited by the maximum oscillator drift between the transmitter and receiver as
i.
            N      nc        <          2                        Δ          f                ⁢                  T          s                      ,
where Δf is the unitless relative amount of oscillator offset
      Δ    f    =                1      -                        f          T                          f          R                        
and Ts is the symbol period in samples.
In addition, due to the integration group delay at the beginning of the reception, while the accumulation of NCI energy ramps up, peaks may be missed at the beginning of each reception, perhaps even many such peaks. Compounding that issue, the negative SNR condition and limited NCI duration may result in many “missing” peaks, i.e., locations throughout the reception that are not apparent above any practical threshold.
It may be desirable to have a receiver timing synchronization technique that addresses the above issues.